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Lisa drove 120 miles, then increased her speed by 30 miles per hour for 270 miles. If the second part of the drive took 1 hour longer than the first part, find her average speed
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Jul 10, 2019
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Lisa drove 120 miles, then increased her speed by 30 miles per hour for 270 miles. If the second part of the drive took 1 hour longer than the first part, find her average speed
Mathematics
college
Justin Dalrymple
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Justin Dalrymple
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Let the speed = r
120/r = the time it took to go the first 120 hours.
270/(r + 30) = the time it took to go the second part of the trip.
270/(r + 30) - 120/r = 1
Multiply through by r*(r + 30)
270 * r - 120*(r + 30) = 1* r*(r + 30) Remove the brackets.
270r - 120r - 3600 = r^2 + 30r Collect left like terms.
150r - 3600 = r^2 + 30r Transfer the left side to the right.
0 = r^2 - 120r + 3600 This should factor
(r - 60)(r - 60) = 0
r = 60 and r1 = 60
270 / (30 + 60) = 270 / 90 = 3 hours
120 / 60 = 2 hours. So far so good.
Now we need to get the average speed.
d = 270 + 120
d = 390
t = 3 + 2
t = 5 hours.
Average speed = d / t
Average speed = 390 / 5
Average speed = 78 miles / hour.
Yajneshwar Mandal
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Jul 13, 2019
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Yajneshwar Mandal
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